CAMBRIDGE - Locked out of his church on charges of blasphemy and left to work as a tour guide, the Rev. T. Lawrence Shannon – the central character in Tennessee Williams’ “The Night of the Iguana,” now in a very worthy new mounting at the American Repertory Theatre in Cambridge – is anxious to exhale when he arrives at the down-on-its-luck Hotel Costa Verde on the Pacific Coast of Mexico.

With his group of Baptist women’s college teachers in tow and audibly upset by yet another change in their itinerary, Shannon is also seeking his own refuge south of the border, trying to stave off both a second nervous breakdown and the carnal temptations that have left him accused of statutory rape.

Set in 1940, “The Night of the Iguana” premiered on Broadway in 1961 and was Williams’ last real success. While his brilliance is often defined by indelible female characters like Amanda Wingfield in “The Glass Menagerie,” Blanche DuBois in “A Streetcar Named Desire,” and Maggie the Cat of “Cat on a Hot Tin Roof,” Williams also created a canon of unforgettable male characters.

The esoteric Shannon – played first by Patrick O’Neal on Broadway, later by Richard Burton in the 1964 film adaptation, and now by Bill Heck – may not have much in common with the brutish Stanley Kowalski of “Streetcar,” but he does bear some similarity to the itinerant ladies’ man Chance Wayne in “Sweet Bird of Youth,” and to the fallen football hero Brick Pollitt in “Cat.” Like them, his physicality and brooding manner make him a fascination for those around him.

Heck’s Shannon is lean, languorous, and as sexy as any man of the cloth should be, but his restlessness makes it clear that he’s not comfortable in his own skin. In Heck’s compelling portrayal, we can see and feel Shannon’s struggles – with his beliefs, the bottle, and his proclivity for underage women – as they roil through him.

Originated on Broadway by Bette Davis and on film by Ava Gardner, the character of Maxine Faulk, recently widowed and now running the Costa Verde on her own, is played here by Dana Delany. A two-time Emmy Award winner for the television series “China Beach,” Delany is a fine actress, but even with her blouse askew she is too wholesome to be fully believable as the bawdy proprietor of a second-rate inn with both a predatory interest in Shannon and a pair of buff bellboys (Kiki Macan and Mike Turner) at her beck and call.

As Shannon clings to his sanity, often while also clinging to Maxine’s well-used hammock, he is circled not only by her and by Charlotte Goodall (an innocent-faced Susannah Perkins), the teenager with whom he was inappropriately involved, but also by Hannah Jelkes, an unmarried, nomadic artist portrayed here by the wondrous Amanda Plummer.

Thirty-five years after she won a Tony Award as the novice nun and title character in “Agnes of God” – which had a memorable pre-Broadway run at Boston’s Wilbur Theatre – Plummer’s mastery of singular, ethereal characters continues unabated. The beautifully written act-two scene in which a bond is both found and formed between the sensitive but strong Hannah and the tortured Shannon is a vivid reminder of what made Williams one of the greatest American playwrights of the 20th century.

And with this production perhaps Broadway-bound – as evidenced by the presence of Tony-winning producer Jeffrey Richards in the opening-night audience – the cast also includes the iconic James Earl Jones as Nonno, Hannah’s aged poetry-writing-and-reciting grandfather, and the always interesting Elizabeth Ashley as Judith Fellowes, Charlotte’s avenging guardian and a persistent thorn in Shannon’s side.

Ashley – Maggie in a 1974 Broadway revival of “Cat,” and Amanda in a Hartford Stage production of “Menagerie” that came to the American Repertory Theater’s Loeb Drama Center in 2001 – knew Williams personally and knows his language intimately. In this production, she tucks away her customary sexiness to imbue the sensible-shoe-wearing Judith with a faultless authenticity.

Also adding realism and eeriness to the story’s World War II timing is a family of German tourists (Richmond Hoxie, Stacia Fernandez, Hannah Sharafian, and Ben Winter) who gleefully march their way to and from the beach, stopping occasionally to catch the news on the radio and cheer on their führer, Adolf Hitler.

The drama is in the very capable hands of director Michael Wilson, who, during his time as artistic director at Hartford Stage produced and directed a 10-year Williams cycle which included a 2003 mounting of “Iguana.” Wilson knows well how to cast and pace a Williams play so that not a word is lost, nor a nuance missed.

A Tony-winning technical team includes scenic designer Derek McLane, whose frayed set pieces perfectly convey the heat, dust, and disappointment of this tired and timeworn Mexican hotel, and costume designer Catherine Zuber, who has given each character distinctive garb. David Lander’s mood-setting lighting and John Gromada’s solid, if not always spot-on, sound design also add measurably to the proceedings.